So talking of encryption, if Chad and Lori had encrypted phones could they be communicating without the knowledge of LE ?
Yes, but that does not require an encrypted phone. There are lots of ways to have secure communications these days that even the best intelligence agencies cannot crack.
Would their phones still ping?
Yes, but they could easily have gotten burner phones.
Would both recipient and sender need encrypted phones? Eg. Lawyer communications.
Yes/no. Hard to answer this question simply. If both ends are not secure then the communication is not secure. An encrypted phone does not guarantee the connection is secure and an secure connection does not protect the information on teh phone. They are kind of both required for complete communication security.
Encrypting the phone prevents anyone (hackers, scammers, law enforcement, the CIA, NSA, etc.) from accessing the information stored on your phone like passwords, account numbers, credit card records, contacts, etc. A secure connection makes it so that if someone intercepts the transmission they cannot understand what is being said.
US courts have ruled that law enforcement cannot force someone to unlock their phone by password, PIN, iris, fingerprint, swipe pattern, etc. And for all practical purposes, an encrypted phone cannot be accessed by law enforcement. If the NSA can't do it for terrorists, I'm pretty sure the RPD can't do it.
Records of who you called, length of call, and so forth are, in the US, partly protected and wholly unprotected depending on the circumstance. There are a lot of things law enforcement does that are increasingly being ruled illegal. Things like faking a cell tower to intercept a call between criminals, for example using a device called a "stingray" is legal BUT, when such devices are used the cases are often dropped because the defense cannot be provided with adequate discovery to challenge the evidence. I say this because those records are business records of the cell phone company. Law enforcement is not automatically entitled to them but in most cases they can get access to this metadata.
If they have been in Hawaii for two months, how have they been communicating with the lawyer or whoever has the kids, if they are still alive? Regular landline phones? CB radio? Email?
I have no idea but there are many apps that offer secure communication. There is no reason they needed to hide communication with their lawyer. That could not be used against them. But if they wanted to, I'm guessing a burner phone would be easiest.